Hold-up problem

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This article deals with a situation between exactly two contractual partners who are subject to a lock-in effect. For the situation of collective action by a large number of market participants leading to market failure, see the holdout problem .

The hold-up problem (from English hold up for "attack" or "disruption") is described in economics , especially in contract theory , as a situation in which one assumes two contractual partners , the ex ante a business relationship enter. The two partners are subject to the lock-in effect , i. In other words, they are bound to one another in this business relationship. This creates the risk of ex post opportunistic behavior. One party can impose trading conditions on the other that do not adequately cover their initial investment costs. Since there is no way to evade, this unfavorable condition must be accepted. By anticipating this problem, lower investments are made ex ante than would be efficient .

Explanation

Two contractual partners enter into a business relationship with regard to a good , one being the seller and the other a buyer. One partner depends on the performance of the other.

Since the asset to be exchanged cannot be fully described at first, neither the costs nor the willingness to pay can be precisely determined ex ante . Therefore, usually only an incomplete contract is drawn up between the parties. Usually the seller is obliged to make investments before trading. If the buyer's willingness to pay is higher than the cost of the goods, an exchange occurs. The costs can be precisely determined at the time of the exchange. The decisive factor now is who has the bargaining power . This can then tend to post-contractual opportunism. That is, he will enforce trading conditions that do not adequately cover the other's investments that have already been made. If the bargaining power rests with the buyer, the seller will not make those investments ex ante that would have maximized welfare , as he foresaw the risk of hold-up.

Hold-up problems generally describe situations in which contracts are concluded with incomplete information about the possibilities, interests and intentions of the other and only then become apparent ex post and lead to the fact that the right incentives are not created ex ante in turn leads to underinvestment.

The hold-up problem in the trading model

In this model it is initially assumed that the two companies under consideration are subject to the lock-in effect . One company sells an (intermediate) product that is not divisible and the other buys it.

The parameters of the model are defined as follows:

${\displaystyle q}$describes the level of trade, with trade and non- trade . The seller incurs costs in the production of the goods and the buyer can use at most one unit of the goods with which he achieves a return of . The retail price of the goods is included . ${\displaystyle q=1}$ ${\displaystyle q=0}$ ${\displaystyle c}$ ${\displaystyle v}$ ${\displaystyle p}$

The seller's profit function is now

${\displaystyle \pi _{1}(p,q)=(p-c)q}$

And the buyer's

${\displaystyle \pi _{2}(p,q)=(v-p)q}$

It is also assumed that and thus the production of a unit of the good is always efficient. The buyer should also receive a share of the trade surplus, which is also a measure of his bargaining power. The price is then included ${\displaystyle v>c}$ ${\displaystyle a\epsilon (0,1)}$

${\displaystyle P=(1-a)v+ac}$

The model is extended by the fact that the buyer can make investments that increase his return. The yield is now described with the function that has the following properties: and d. That is, the marginal return on additional investments is positive and falling in the investment level. It is also assumed that trade and production are worthwhile through . With the investments, the buyer also incurs costs , while and , the investments increase slightly monotonously . ${\displaystyle i\geq 0}$ ${\displaystyle v(i)}$ ${\displaystyle v'>0}$ ${\displaystyle v''<0}$ ${\displaystyle v(0)>c}$ ${\displaystyle k(i)}$ ${\displaystyle k(0)=k'(0)=0}$ ${\displaystyle k''\geq 0}$

The buyer's profit function looks like this:

${\displaystyle \pi _{2}(q,p,i)=(v(i)-p)q-k(i)}$ .

Now consider the total profit,

${\displaystyle \Pi (q,i)=\pi _{1}(q,p)+\pi _{2}(q,p,i)=q(v(i)-c)-k(i)}$

which is maximized in order to determine the efficient or “first-best” solution.

So that's because trading in the model is always efficient. With an optimal investment level, marginal return is equal to the marginal costs of a marginal investment, which is why this marginal condition exists . ${\displaystyle q^{*}=1}$ ${\displaystyle v'(i^{*})=k'(i^{*})}$

It is now assumed that the buyer's investments are not observable and cannot be contractually defined, nor can a long-term contract be drawn up.

This means that the level of trade and the price are only negotiated ex post. The higher the bargaining power of the buyer, the higher he invests, because his investments increase the surplus from which he will benefit later. However, his investment still remains below the investment of the efficient solution, since the seller and buyer share the surplus. For an efficient investment, the buyer would need the encouragement of the entire increase in income as an incentive. The incentives to invest are thus distorted and underinvestment occurs, efficiency is no longer achieved and the hold-up problem arises .

Examples

Simple example

A supplier and a buyer have a business relationship. It is assumed that the supplier invests in a special machine that exclusively produces special parts for this customer, so that there is a high quasi-pension . Only the supplier price is contractually agreed, but not the quantity of the product, as there are high fluctuations in demand for the end products. There is also no detailed quality agreement due to the high transaction costs . In this example, the supplier is dependent on the buyer, but the buyer is not dependent on the supplier if it is assumed that he could also obtain his parts from another manufacturer. Thus, the supplier is in danger of being exploited by his customer with the special machine in the amount of the quasi-pension, which is the hold-up problem . Now the buyer is in the power to demand a price reduction or other demands from the supplier, as he can threaten to change suppliers or to only buy such small quantities of the goods that the supplier's fixed costs are covered. From a rational point of view, the supplier will only dissolve the contractual relationship if the buyer receives the entire quasi-pension and he cannot even cover his costs.

However, there is also the possibility that the supplier does not make any transaction-specific investments ex ante without any advance payments by the buyer, such as B. Participation in the investment costs , as he is aware of the hold-up risk that occurs .

Historical example

A popular historical example is the US auto industry of the 1920s ( heavily disputed by Coase , 2000). Fisher Body had an exclusive contract with General Motors (GM) for the supply of body parts. It is alleged that Fisher Body took advantage of the hold-up problem by receiving payments 17% over their costs, moving the body panels for GM away from its assembly plant, and manufacturing them inefficiently. The possibility of this hold-up problem arose because at the time of the contract it was not foreseeable that the demand for cars would grow so rapidly. In addition, the takeover of Fisher Body to GM is argued as a result of the hold-up problem .

solutions

• The standard solution of the transaction cost approach consists of vertical integration , in which one transaction partner on one production level buys the other transaction partner on the upstream or downstream production level or both transaction partners merge.

• Another possible solution would be for the investments to be made periodically. This is intended to cover the investor's costs, because he would not invest again if the income was insufficient. The potential "fraudster" is deterred by the possibility of a future hopeless profit and makes the necessary payout to the investor.

General solutions to the trading model

• The efficient solution is implemented through a contract between the two partners. This is possible if the investment can be checked by a court. If the buyer does not make the efficient investment , he will have to pay penalties to the seller. ${\displaystyle i}$ ${\displaystyle i=i^{*}}$

• The efficient solution is achieved through a long-term contract that describes the goods to be delivered and their price . A trade between the two parties arises when there is between and . It then applies and the buyer chooses to maximize his profit, since it is contractually fixed and therefore independent of his investment. ${\displaystyle p}$ ${\displaystyle p}$ ${\displaystyle c}$ ${\displaystyle v(i)}$ ${\displaystyle q=q^{*}}$ ${\displaystyle i=i^{*}}$ ${\displaystyle p}$

Optimal Contracts - The Hart and Moore Model (1998)

In this model, as before, there is a seller and a buyer who enter into an incomplete contract about their business relationship. The contract includes payment obligations, on the one hand the agreed delivery price when the trade is carried out and on the other hand the compensation in the event of non-execution. In addition, denotes a finite set of conceivable future environmental conditions. The buyer can influence the benefits through an investment , and the seller can influence the costs with his investment . ${\displaystyle {\hat {p}}_{1}}$ ${\displaystyle {\hat {p}}_{0}}$ ${\displaystyle \omega \;\epsilon \;\Omega }$ ${\displaystyle \beta (\sigma )}$ ${\displaystyle v=v(\omega ,\beta )}$ ${\displaystyle c=c(\omega ,\sigma )}$

At the beginning, the benefits and costs are not known with certainty and are therefore random variables. ${\displaystyle v}$ ${\displaystyle c}$

There are three points in time in this model.

Time 0 denotes the conclusion of the contract. All investments will be made up to time 1 and the actors will then experience the actual characteristics of the random variables. It is now possible to initiate renegotiations with the newly acquired information. At time 2 it is then decided whether the agreed payments will be traded or whether there will be a legal dispute.

If no new agreements are reached, the following cases are implemented according to Hart and Moore:

1. If so , there is no trading and the buyer pays the provider ${\displaystyle v<c}$ ${\displaystyle {\hat {p}}_{0}}$
2. If so , then a deal takes place and the buyer pays ${\displaystyle v\geq ({\hat {p}}_{1}-{\hat {p}}_{0})\geq c}$ ${\displaystyle {\hat {p}}_{1}}$
3. If so , then a deal takes place and the buyer pays ${\displaystyle v\geq c>({\hat {p}}_{1}-{\hat {p}}_{0})}$ ${\displaystyle {\hat {p}}_{0}+c}$
4. If so , then a deal takes place and the buyer pays ${\displaystyle ({\hat {p}}_{1}-{\hat {p}}_{0})>v\geq c}$ ${\displaystyle {\hat {p}}_{0}+v}$

Case (1) does not involve trading, since the value of the good is below its production costs and so none of the actors is interested in an exchange. In case of doubt, the court will demand compensation.

In case (2), the trade is advantageous for both parties because the benefit is greater than the price and the latter is greater than its cost.

The third case also entails a trade, as it is generally advantageous with . However, the production costs are so high that it is not worthwhile for the seller to produce at the initial conditions. In the event that no exchange occurs, he can claim in court . This price is higher than the difference between the selling price and the cost, i.e. H. his profit, which is why the buyer will offer him . The supplier is thus indifferent between producing and not producing. Hence, in equilibrium, there will be deal at the renegotiated price. ${\displaystyle v\geq c}$ ${\displaystyle {\hat {p}}_{0}}$ ${\displaystyle {\hat {p}}_{1}}$ ${\displaystyle {\hat {p}}_{0}+c}$

Even in the latter case (4), trading with is efficient, but the original price of is too high in relation to . Therefore the seller lowers his price in equilibrium . Here the customer is indifferent between his alternatives. Again, an exchange is made between the two parties at the new price. ${\displaystyle v\geq c}$ ${\displaystyle {\hat {p}}_{1}}$ ${\displaystyle {\hat {p}}_{0}}$ ${\displaystyle {\hat {p}}_{0}+v}$

In cases (3) and (4), the person who sees the initial conditions as advantageous receives the complete efficiency gains. In other words, in the third case, the provider is compensated in the new negotiation equilibrium to such an extent that the production and thus the efficient behavior is not disadvantageous. In the fourth case, on the other hand, the buyer is compensated in order to achieve efficient behavior.

If you now go back a step and look at the investments made by the two parties, it turns out that, as a rule, no efficient investments are made. This is due to the mutual positive effects that are not taken into account. A marginal increase in the provider's investment leads to a reduction in costs and thus to a lower price. Thus, the entire marginal return on the investment would go to the buyer. This also applies in the opposite case. An increase in the buyer's investment has a positive external effect on the seller. These effects can occur in cases (3) and (4).

However, there are four exceptions to this model in which first-best results can be achieved.

(a) There is a value for which with probability for any investments and ${\displaystyle k}$ ${\displaystyle v\geq k\geq c}$ ${\displaystyle 1}$ ${\displaystyle \beta }$ ${\displaystyle \sigma }$

(b) is independent of ${\displaystyle v(\omega ,\beta )}$ ${\displaystyle \beta }$

(c) is independent of ${\displaystyle c(\omega ,\sigma )}$ ${\displaystyle \sigma }$

(d) and are independent of ${\displaystyle v(\omega ,\beta )}$ ${\displaystyle c(\omega ,\sigma )}$ ${\displaystyle \omega }$

If in the special case (a) a value of is chosen in the initial contract, all externalities are avoided. ${\displaystyle {\hat {p}}_{1}-{\hat {p}}_{0}}$

In case (b), the value of the good is independent of the investment, so a first-best solution can be achieved. This happens when the difference between and is set so high that it exceeds the maximum value of the object. In this way, the seller receives all the resulting pensions and thus has an optimal investment incentive. ${\displaystyle {\hat {p}}_{1}}$ ${\displaystyle {\hat {p}}_{0}}$

Case (c) is the mirror image of case (b) with a difference chosen to be less than the possible cost. ${\displaystyle {\hat {p}}_{1}-{\hat {p}}_{0}}$

The special case (d) has secure production costs and a secure property value, so there are no external effects, as the final prices can be determined before the investments are made.

The model listed by Hart and Moore tries to solve the problem with renegotiation, but it is extreme in that it only gives all the profits from these new negotiations to one side. This is because, on the one hand, there is an exact last point in time for the formulation of an offer, because only at point in time 2 should the exchange bring any benefit. On the other hand, it is because the uncertainty dissipates at time 1 and there is no private information in the renegotiations. This is also efficient for these.

Hart and Moore use extremely restrictive conditions to solve the hold-up problem in order to ensure efficient contract drafting. They only leave an extremely limited scope for drafting the contract and assume that there are no negotiation costs.

literature

• D. Balkenborg, TR Kaplan, T. Miller: A simple economic teaching experiment on the hold-up problem. (= MPRA Paper. No. 24772). 2010. (online)
• Mathias Erlei: institutions, markets and market phases. Mohr Siebeck, Tübingen 1998, ISBN 3-16-147034-6 .
• C. Ewerhart, PW Schmitz: The lock in effect and the hold up problem. (= MPRA Paper. No. 6944). 1997. (online)
• Oliver Hart, John Moore: Property Rights and the Nature of the Firm. In: Journal of Political Economy. Volume 98, No. 6, 1990, pp. 1119-1158.
• Matthias Kräkel: Organization and Management. 5th edition. Mohr Siebeck, Tübingen 2012, ISBN 978-1-283-54170-1 .

Individual evidence

1. ^ Matthias Kräkel: Organization and Management. 5th edition. Mohr Siebeck, Tübingen 2012, ISBN 978-1-283-54170-1 .
2. ↑ D. beams Borg, TR Kaplan, T. Miller: A simple economic teaching experiment on the hold-up a problem. (= MPRA Paper. No. 24772). 2010. (online)
3. ↑ econ.psu.edu